Question

Find the equation of the quadratic function with zeros at -1 and 1 and a vertex at (0,-6)

Answer 1

A polynomial with zeroes at -1 and 1 is a multiple of

`(x-1)(x+1) = x^2-1`

So, your polynomial is something like

`a(x^2-1)`

We can determine the value of a by imposing the passage through (0,-6):

`f(0) = a(0-1)=-a=-6 \iff a=6`

So, the function is

`6(x^2-1)`